Y-Δ transform

The Y-Δ transform, also written Y-delta, Wye-delta, Kennelly’s delta-star transformation, star-mesh transformation, T-Π or T-pi transform, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. In the United Kingdom, the wye diagram is sometimes known as a star. This circuit transformation theory was published by Arthur Edwin Kennelly in 1899



-Y Transformation
The configuration can be converted to and vice versa. To relate and , the resistances between terminals a and b of should be equal to of , and the same is true for the other two resistances, i.e.,

• Convert to : Given , and of a , the three equations can be solved for , and of the corresponding . For example, subtracting the 3rd equation from the sum of the first two, we get expression for . The solutions are:
  
  
  
  
• Convert to : Reversely, given , and of a , the same three equations can also be solved for , and of the corresponding to get:
  
  
  
  The following circuit can be converted into either of the two low equivalent circuits.

The formed by , , and can be converted to a Y, which can then be combined with to get a Y (bottom left) with:



Alternatively, the Y formed by , , and can be converted to a , which can then be combined with to get a (bottom right) with:


The resulting and Y circuits are equivalent as it can be shown they can also be converted to each other with the same system variables.

Attached Files

Y-Δ transform (www.bzupages.com).docx (48.6 KB, 253 views)

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